**Interactive Slope of a line. Click and drag points to see formula in action


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    How to find the slope of a line.

    The slope of a line characterizes the general direction in which a line points.  To findthe slope, you divide the difference of the y-coordinates of a point on a line by the difference of the x-coordinates.

    Slope of vertical and horizontal lines


    • The slope of a vertical line is undefined

      . This is because any vertical line has a x or "run" of zero. Whenever zero is the denominator of the fraction in this case of the fraction representing the slope of a line, the fraction is undefined. The picture below shows a vertical line (x=1)

    • The slope of a horizontal line is zero

      This is because any horizontal line has a . Y or "rise" of zero. Therefore, regardless of what the run is (provided its' not also zero!), the fraction representing slope has a zero in its numerator. Therefore, the slope must evaluate to zero. Below is a picture of a horizontal line--you can see that it does not have any 'rise' to it.
    This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line
    Interactive slope |Interactive Linear Equation
    Related pages: slope intercept form of a line | Erroneous Slope
    Worksheet on Slope Of A Line

     Formula to find the slope of a line  

    Formula for the slope of a line
      Example 1of the Slope of A line
    • The slope of a line through the points (1, 2) and (2, 5) is 3 because every time that the line moves up three (the change in y or the rise) the line moves to the right (the run) by 1.
      • Picture of the slope of a line
      Illustrated Example Two
    • The slope of a line going through the point (1,2) and the point (4,3) is 1/3.
      • Graph of the slope of a line
    There is a fundamental point to remember about calculating slope.
    • Every line has a consistent slope. In other words, the slope of a line never changes. This fundamental idea means that you can choose ANY two points on a line to find the slope. This should intuitively make sense with your own understanding of a straight line. After all, if the slope of a line could change, then it would be a zigzag line and not a straight line.
    This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line

    Interactive Slope


    Click and drag around either of the points below, as you move the points around, you can see the slope of the line will adjust accordingly.
    This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line
    Practice Problems
    Find the slope of A line Given Two Points

    Practice Problem 5) What is the slope of a line that goes through the points (10,3) and (7 , 9) ?

     Answer 


    Practice Problem 6) A line passes through (4, -2) and (4 , 3). What is its slope?

     Answer 



    Practice Problem 7) A line passes through (2, 10) and (8 , 7). What is its slope?

     Answer 


    Practice Problem 8) A line passes through (7,3) and (8 , 5). What is its slope?

     Answer 


    Practice Problem 9) A line passes through (12,11) and (9 , 5). What is its slope?

     Answer 



    Practice Problem 10) What is the slope of a line that goes through (4, 2) and (4, 5)?

     Answer 

    Slope Practice -- Problem Generator

    You can practice solving this sort of problem as much as you would like with the slope problem generator below. It will randomly generate numbers and ask for the slope of the line through those two points. You can chose how large the numbers will be by adjusting the difficulty level.



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